IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v117y2007i11p1642-1662.html
   My bibliography  Save this article

Stability of utility-maximization in incomplete markets

Author

Listed:
  • Larsen, Kasper
  • Zitkovic, Gordan

Abstract

The effectiveness of utility-maximization techniques for portfolio management relies on our ability to estimate correctly the parameters of the dynamics of the underlying financial assets. In the setting of complete or incomplete financial markets, we investigate whether small perturbations of the market coefficient processes lead to small changes in the agent's optimal behavior, as derived from the solution of the related utility-maximization problems. Specifically, we identify the topologies on the parameter process space and the solution space under which utility-maximization is a continuous operation, and we provide a counterexample showing that our results are best possible, in a certain sense. A novel result about the structure of the solution of the utility-maximization problem, where prices are modeled by continuous semimartingales, is established as an offshoot of the proof of our central theorem.

Suggested Citation

  • Larsen, Kasper & Zitkovic, Gordan, 2007. "Stability of utility-maximization in incomplete markets," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1642-1662, November.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:11:p:1642-1662
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00091-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Friedrich Hubalek & Walter Schachermayer, 1998. "When Does Convergence of Asset Price Processes Imply Convergence of Option Prices?," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 385-403, October.
    2. He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
    3. L.C.G. Rogers, 2001. "The relaxed investor and parameter uncertainty," Finance and Stochastics, Springer, vol. 5(2), pages 131-154.
    4. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    5. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    6. Elyès Jouini & Clotilde Napp, 2004. "Convergence of utility functions and convergence of optimal strategies," Finance and Stochastics, Springer, vol. 8(1), pages 133-144, January.
    7. Trojani, Fabio & Vanini, Paolo, 2002. "A note on robustness in Merton's model of intertemporal consumption and portfolio choice," Journal of Economic Dynamics and Control, Elsevier, vol. 26(3), pages 423-435, March.
    8. Nicole El Karoui & Monique Jeanblanc‐Picquè & Steven E. Shreve, 1998. "Robustness of the Black and Scholes Formula," Mathematical Finance, Wiley Blackwell, vol. 8(2), pages 93-126, April.
    9. Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short‐Sale Constraints: the Finite‐Dimensional Case1," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10, July.
    10. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    11. Freddy Delbaen & Walter Schachermayer, 1998. "A Simple Counterexample to Several Problems in the Theory of Asset Pricing," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 1-11, January.
    12. repec:dau:papers:123456789/355 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Constantinos Kardaras & Gordan Zitkovic, 2007. "Stability of the utility maximization problem with random endowment in incomplete markets," Papers 0706.0482, arXiv.org, revised Mar 2010.
    2. Mahan Tahvildari, 2021. "Forward indifference valuation and hedging of basis risk under partial information," Papers 2101.00251, arXiv.org.
    3. Feyzullah Egriboyun & H. Soner, 2010. "Optimal investment strategies with a reallocation constraint," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(3), pages 551-585, June.
    4. Carole Bernard & Franck Moraux & Ludger R�schendorf & Steven Vanduffel, 2015. "Optimal payoffs under state-dependent preferences," Quantitative Finance, Taylor & Francis Journals, vol. 15(7), pages 1157-1173, July.
    5. Gerrard, Russell & Kyriakou, Ioannis & Nielsen, Jens Perch & Vodička, Peter, 2023. "On optimal constrained investment strategies for long-term savers in stochastic environments and probability hedging," European Journal of Operational Research, Elsevier, vol. 307(2), pages 948-962.
    6. Julien Hugonnier & Dmitry Kramkov, 2004. "Optimal investment with random endowments in incomplete markets," Papers math/0405293, arXiv.org.
    7. L. Rüschendorf & Steven Vanduffel, 2020. "On the construction of optimal payoffs," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(1), pages 129-153, June.
    8. Jessica A. Wachter, 2010. "Asset Allocation," Annual Review of Financial Economics, Annual Reviews, vol. 2(1), pages 175-206, December.
    9. Schroder, Mark & Skiadas, Costis, 2005. "Lifetime consumption-portfolio choice under trading constraints, recursive preferences, and nontradeable income," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 1-30, January.
    10. repec:dau:papers:123456789/5374 is not listed on IDEAS
    11. Jouini, Elyes, 2001. "Arbitrage and control problems in finance: A presentation," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 167-183, April.
    12. Chenxu Li & O. Scaillet & Yiwen Shen, 2020. "Decomposition of Optimal Dynamic Portfolio Choice with Wealth-Dependent Utilities in Incomplete Markets," Swiss Finance Institute Research Paper Series 20-22, Swiss Finance Institute.
    13. Sanjiv Ranjan Das & Rangarajan K. Sundaram, 2002. "An approximation algorithm for optimal consumption/investment problems," Intelligent Systems in Accounting, Finance and Management, John Wiley & Sons, Ltd., vol. 11(2), pages 55-69, April.
    14. Chen, An & Vellekoop, Michel, 2017. "Optimal investment and consumption when allowing terminal debt," European Journal of Operational Research, Elsevier, vol. 258(1), pages 385-397.
    15. Oleksii Mostovyi, 2015. "Necessary and sufficient conditions in the problem of optimal investment with intermediate consumption," Finance and Stochastics, Springer, vol. 19(1), pages 135-159, January.
    16. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    17. Yuanrong Wang & Tomaso Aste, 2021. "Dynamic Portfolio Optimization with Inverse Covariance Clustering," Papers 2112.15499, arXiv.org, revised Jan 2022.
    18. André Palma & Jean-Luc Prigent, 2009. "Standardized versus customized portfolio: a compensating variation approach," Annals of Operations Research, Springer, vol. 165(1), pages 161-185, January.
    19. Christoph Belak & An Chen & Carla Mereu & Robert Stelzer, 2014. "Optimal investment with time-varying stochastic endowments," Papers 1406.6245, arXiv.org, revised Feb 2022.
    20. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    21. X. Chao & K. Lai & Shou-Yang Wang & Mei Yu, 2005. "Optimal Consumption Portfolio and No-Arbitrage with Nonproportional Transaction Costs," Annals of Operations Research, Springer, vol. 135(1), pages 211-221, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:117:y:2007:i:11:p:1642-1662. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.